What is Cos: Definition and 318 Discussions

Cos Cob is a neighborhood and census-designated place in the town of Greenwich, Connecticut. It is located on the Connecticut shoreline in southern Fairfield County. It had a population of 6,770 at the 2010 census.Cos Cob is located on the western side of the mouth of the Mianus River. The American Impressionist Cos Cob Art Colony flourished in the late 19th and early 20th centuries. An offshoot of the group, the Greenwich Art Society, continues to support local artists in town.
The town of Greenwich is one political and taxing body, but consists of several distinct sections or neighborhoods, such as Banksville, Byram, Cos Cob, Glenville, Mianus, Old Greenwich, Riverside and Greenwich (sometimes referred to as central, or downtown, Greenwich). Of these neighborhoods, three (Cos Cob, Old Greenwich, and Riverside) have separate postal names and ZIP codes. From 1883 to 1885, the official post office name of Cos Cob was Bayport.
In 2015, Forbes ranked Cos Cob the 287th wealthiest place in the US with a median house sale price of $1,329,107.

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  1. W

    Converting from sin to cos appropriately with phasors

    My transmissions line class often features problems where the voltage is expressed as a sin, not a cos. Obviously a phase shift of pi/2 is sufficient to convert between the two. However, I have trouble understanding when adding pi/2 is appropriate as opposed to subtracting pi/2. As per my...
  2. L

    Calculate the limit cos(x)/sin(x) when x approaches 0

    Hi, I need to check whether the limit of the following function exists or not I have now proceeded as follows to look at the right-sided and left-sided limit i.e. ##\displaystyle{\lim_{x \to 0^{+}}}## and ##\displaystyle{\lim_{x \to 0^{-}}}## To do this, I drew up a list in which I move from...
  3. R

    How to find out the sin value from cos

    First off sorry if something doesn't make sense, english is not my native language. I know i should start with sin2 α + cos2 = 1, but ant really continue from it. i am being confused by cos α = √5/3 since i know it isn't found in normal trig tables. So my problem is how to find out values of...
  4. S

    I Derive the probability of spin at arbitrary angle is cos( )

    From Dr. Leonard Susskind's Stanford Lecture: Quantum Entanglement, Lecture 4, he sets up a "given particle is spin up along n (arbitrary direction) and discusses : what is probability we measure up along another arbitrary m directionHe does all of the setup, - calculates the eigenvectors and...
  5. karush

    MHB -7.8.98 amplitude period PS VS graph. of cos eq

    Find amplitude, period, PS, VS. then graph. ok I think these are the plug ins we use $Y_{cos}=A\cos\left[\omega\left(x-\dfrac{x \phi}{\omega} \right)\right]+B \implies A\cos\left(\omega x-\phi\right)+B \implies T=\dfrac{2\pi}{\omega} \implies PS=\dfrac{\phi}{\omega}$ ok I wanted to do...
  6. igorrn

    Area between two curves (x = cos(y) and y = cos (x))

    I tried this: X = cos(y) → y = arccos(x) for x E(-1,1) and y E (0,2) Then: There's a point I(Xi,Yi) in which: Cos(Xi) =Arccos(Xi) Then I said area1 (file: A1) A1 = ∫cosx dx definite in 0, Xi And A2 (file:A2): A2 = ∫cosy dy definite in 0, Yi And the overlapping area as A3 (file: A3): A3 = ∫Yi dx...
  7. karush

    MHB 33. Express sin 4x in terms of sin x and cos x

    Express function as a trigonometric function of x $$\sin(4x)$$ use $\sin2a=2\sin a\cos a$ then $$\sin4x=2\sin 2x\cos 2x$$ with $\cos(2x) = \cos^2(x)-\sin^2(x)$ replace again $$\sin 4x=4\sin x\cos x+\cos^2(x)-sin^2(x)$$ ok not real sure if this is what they are...
  8. Morbidly_Green

    Finding the Sine Representation of an Odd Function Using Fourier Series

    I am attempting to find the sine representation of cos 2x by letting $$f(x) = \cos2x, x>0$$ and $$-\cos2x, x<0$$ Which is an odd function. Hence using $$b_n = \dfrac{2}{l} \int^\pi _0 f(x) \sin(\dfrac{n\pi x}{l})dx$$ I obtain $$b_n = \dfrac{2n}{\pi} \left( \dfrac{(-1)^n - 1}{4-n^2} \right)$$...
  9. Matt Benesi

    B Periodic smooth alternating series other than sin and cos

    1) Are there any periodic alternating series functions other than sine and cosine (and series derived from them, like the series for cos(a) * cos(b))? 2) What is the following series called when x is (0,1) and (1,2]? Quasiperiodic? Semi? \sum_{n=0}^\infty \, (-1)^n \...
  10. E

    MHB Evaluate cos 2(theta) and sin 2(theta)

    So my math professor gave us a study guide for the final but he's not aloud to give us the answers so I have no idea if my answers are correct or not. So if a few people could let me know what they got after trying this that would be great. If tan(theta) = -2[sqrt(2)], and theta is between 270...
  11. D

    How to find the expectation value of cos x

    Homework Statement If x is a continuous variable which is uniformly distributed over the real line from x=0 to x -> infinity according to the distribution f (x) =exp(-4x) then the expectation value of cos 4x is? Answer is 1/2 Follow· 01 Request Homework Equations the expectation value of any...
  12. Arman777

    Python Graphing a cos function

    r = np.arange(0,400,0.1) t = np.cos(r)+10 plt.plot(r,t) How can I use the range of the cos function to look like this
  13. F

    Graph the Cartesian equation: x = 2 sin t, y = 4 cos t

    Homework Statement Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction...
  14. Entertainment Unit

    Integral of 1/(a sin^2 x + b sin x cos x + c cos^2 x)

    Homework Statement If ##a \neq 0##, evaluate the integral $$\int \frac {dx} {a~\sin^2~x + b~\sin~x~\cos~x + c~\cos^2~x}$$ (Hint: Make the substitution ##u = \tan x## and consider separately the cases where ##b^2 - 4ac## is positive, zero, or negative.) The Attempt at a Solution $$\int \frac...
  15. Mr Davis 97

    I Linear combination of sin and cos

    I have before me that ##\cos 2x + \sin 2x = \sqrt{2} \cos (2x - \pi / 4)##. Where does this expression on the right come from? I tried to look on the internet but I couldn't really articulate it well enough to find anything on it.
  16. K

    Values of sin and cos (rad and deg)

    Homework Statement I am little confused. Value of used to be sin(0) = 0 = cos(1) sin(1) = 1 = cos(0) Homework EquationsThe Attempt at a Solution Now when I use google calculator I use rad or degree I do not get solid 1 and 0. for example sin(0)= 0 deg =0rad sin(1)= .841 deg = 0.017 rad...
  17. R

    Rewriting cos function as sine function

    Homework Statement So in an AC circuit with inductance, I found I = (-ε_{max} cos(ωt)) / ωL I want to rewrite this as a sine function.Homework EquationsThe Attempt at a Solution I can ignore ε_{max} / ωL and work with -cos(ωt) I set ωt = θ I know cos(θ) = sin(θ+pi/2) so -cosθ =...
  18. E

    MHB Differential equation w/ cos and sin

    It would be wonderful if someone could please help with the following question as I don't even know where to begin y=y(x), where x^2 cos y + sin(3x-4y) =3Thank you :)
  19. rumborak

    Cosine Button Convergence: Degrees vs Radians

    This is of course just a silly exercise on a calculator, but it is intriguing that when operating in either degrees or "grad", hitting the cosine button will converge incredibly fast, whereas in radians it is a lot slower. Anybody have a good idea why?
  20. baby_1

    Bessel function transformation and also cos variation

    Homework Statement In a article I have found this transformation (exp to bessel function) . I have two questions. Homework EquationsThe Attempt at a Solution a)where did the Cos go after setting n=1 and n=-1 ? in the third equations ( it is equal to -wmt-pi/2)? why?) b)how did the writer...
  21. Mr Davis 97

    I Small angle expansions for sin, cos, and tan

    From the Wikipedia article https://en.wikipedia.org/wiki/Small-angle_approximation, it says that they are "second-order approximations." What makes all three second order? Shouldn't sin and tan be first-order and cos be second-order?
  22. H

    Find theta given known cos and sin....

    Homework Statement Homework Equations cos 2theta = costheta^2 - sintheta^2 The Attempt at a Solution cos2theta = 1 2theta = 0, 2phi but i get wrong answer.. how is it?
  23. SamRoss

    B Not following an integral solution

    In the image below, why is the third line not \frac {ln(cosx)} {sinx}+c ? Wouldn't dividing by sinx be necessary to cancel out the extra -sinx that you get when taking the derivative of ln(cosx)? Also, wouldn't the negatives cancel?
  24. John Dalton

    B Understanding the Meaning of Sin, Cos, and Tan in Trigonometry

    I am eager to learn trigonometry. I have to be introduced to terms such as-sin,cos,tan,cosec etc. The internet"s explanation is going over my head. Can someone make them understand to me individually with the meaning of titha.(I cannot show its symbol , as it is not on the keyboard.) I will...
  25. Vital

    Graph r = 6 cos() issues with plotting on xy-plane

    Homework Statement Hello! Last week I have came here for the help related to this problem. I am creating a new thread to describe the issue more precisely. I will be grateful for your help and explanation. I post the explanation for the book first accompanied by attached pictures, and below I...
  26. Vital

    Graphs of sin and cos, how to set points for x values

    Homework Statement Hello! I am at the topic on graphing trigonometric functions. Exercises are rather easy at this point, but I have a problem deciphering how authors of the book choose points for x values. Please, take a look at few examples (including screen shots I attach), and, please...
  27. Mr Davis 97

    Partial fraction decomposition with cos() in the numerator

    Homework Statement See below Homework EquationsThe Attempt at a Solution I am looking at a particular integral, and to get started, my text gives the indication that one should use partial fraction decomposition with ##\displaystyle \frac{\cos (ax)}{b^2 - x^2}##. Specifically, it says "then...
  28. Mr Davis 97

    Deriving the sum of sin and cos formula

    Homework Statement Show that ##a \sin x + b\cos x = c \sin (x + \theta)##, where ##c = \sqrt{a^2 + b^2}## and ## \displaystyle \theta = \arctan (\frac{b}{a})## Homework EquationsThe Attempt at a Solution We see that ##c \sin (x + \theta) = c \cos \theta (\sin x) + x \sin \theta (\cos x)##. So...
  29. paulmdrdo1

    MHB Cos Trig Identity: Deriving Formula for Circuits Analysis

    Hello. Do you guys know if there is an identity related to this expression \cos(A+B)\cos(A+C) If so, can you help me how to derive it? I need it for the derivation of the formula from my circuits analysis course. Thanks.
  30. Albert1

    MHB Find tan 15° and cos 72° (using geometry)

    find : (1)$ tan \,\, 15^o$ (2)$cos\,\,72^o$ (using geometry)
  31. S

    I What is the significance of calculating the average value of cos?

    In kinetic theory, the number of molecules hitting a unit area of a surface per unit time with speeds between v and v + dv and angles between \theta and \theta + d \theta is found to be a function of sin(theta) and cos(theta). There will often be a practice problem asking to show that the...
  32. C

    How to calculate the gravity on a hill?

    The question is about a box with no movement standing on a hill. The hill has an angle of 25 degrees. The box has a mass of 40 kg. 1. Calculte the gravity This I still get: F= M x A = 40 x 9,81 = 3,9 x 10^2 The next question tough: 2. Calculate the component Fgravity,x off the gravity...
  33. C

    Curvature of r(t) = (3 sin t) i + (3 cos t) j + 4t k

    Homework Statement [/B] find the curvature of the vector valued function r(t) = 3sint i + 3cost j +4t k Homework EquationsThe Attempt at a Solution For the unit tangent vector , i got T(t) = (3cost i -3sint j +4k) / sqrt (9 ((sint)^2 ) + 9 ((cost)^2 ) + 4^2 ) = (3cost i -3sint j +4k) / 5 For...
  34. V

    Components of a force. When do I use cos or sin?

    Here is an example of a problem I am having trouble with. I need to find the i, j, k of A. I have no issues with finding the components for B, but A I just can't wrap my head around when to use cos or sin. Especially here with double projection. I know that A is : (-10 cos70 sin30, 10 cos70...
  35. A

    B How do you know if you need cos or sin?

    When solving a problem about shooting a cannon ball, why is the velocity in the x direction multiplied by cos and velocity in the y (vertical) direction multiplied by sin? like in the last example here...
  36. M

    MHB Find cos theta and tan theta using sin theta

    If sin \theta =\frac{4}{5} , find cos \theta and tan \theta Can you help me to solve. :) Many thanks :)
  37. I

    Double integral of gaussian times mod cos function

    Homework Statement I want to evaluate the following definite integral of the form, I = \int\limits_{x = -\infty}^{\infty}\int\limits_{y = -\infty}^{\infty} e^{-ax^2} e^{-by^2} | \cos(c x + d y)| dx dy where a, b, c, and d are constants, as part of a larger problem I am doing, Homework...
  38. S

    MHB Find Volume of Revolved Region: [-pi/2, pi/2] & y= cos x & y = -cos x

    Find the volume of the solid generated by revolving the region enclosed by y= cos x and y = -cos x for [-pi/2, pi/2] about the line y=2pi.
  39. U

    Simultaneous equation involving cos, sin

    Homework Statement i have solve a engineering problem until this part I'm stuck C cos 30 - 1.375 cosθ = 0 ----(1) C sin 30 + 1.375 sin θ = 15 ---(2) . i have 2 unknown C and θ, however the change to cos to sin or via versa make me lost because of my poor mathematic Homework Equations The...
  40. anemone

    MHB Cos (π/7) is a root to a cubic equation

    Prove that $\cos \dfrac{\pi}{7}$ is a root of the equation $8x^3-4x^2-4x+1=0$.
  41. Oaxaca

    Complex Conjugates with sin and cos

    I am rather new to the whole idea of complex conjugates and especially operators. I was trying to understand the solution to a problem I was doing, but the math is confusing me rather than the physics. In the last row of calculations, why does the sin change to a cos, and the d/dx change to...
  42. Z

    Separate Variable Homework: Solutions & Equations

    Homework Statement m1v1=m1v1'cosa+m1/2v2'cosB 0=m1v1'sina-(m1v2'sinB/2) m1v1^2=m1v1'^2+(m1v2'^2)/4 Homework Equations The solution in my book is v2'=2v1sqrt(3) The Attempt at a Solution I thought to separate v1' at the firts and put it at the second, but I don't know how to change sin and cos then.
  43. ognik

    MHB Exploring the Convergence of p^n Cos (nx) and p^n Sin (nx)

    They ask for both $ \sum_{n=0}^{\infty} p^n Cos nx, also \: p^n Sin (nx) $ I'm thinking De Moivre so \sum_{n=0}^{\infty}p^n (e^{ix})^n = \sum_{n=0}^{\infty} p^n(Cos x + i Sin x)^n= \sum_{n=0}^{\infty} (pCos x + ip Sin x)^n I also tried a geometric series with a=1, $r=pe^{ix}$ But those...
  44. ognik

    MHB Finding \sum_{n=0}^{N-1} Cos (nx)

    Hi - going in circles about a step in an example, to find $ \sum_{n=0}^{N-1} Cos (nx) $ The book says we find \sum_{n=0}^{N-1} \left( e^{ix} \right)^n = \frac{1-e^{iNx}}{1-e^{ix}} , then take the real part. But I see $ \sum_{n=0}^{N-1} \left( e^{ix} \right)^n $ as a geometric series with...
  45. ryanuser

    Cos(-pi/4) & Sec(pi/4): What's the Difference?

    Why 1 divided by cos(pi/4)=cos(-pi/4)? Is it wrong to say 1/cos(pi/4)=sec(pi/4)? Thanks
  46. Taryn1

    MHB Sum or difference formula (sin, cos, and tan)

    So I'm supposed to find the exact values of the sine, cosine, and tangent of an angle by using a sum or difference formula ( i.e. sin(x+y)=sin(x)cos(y)+cos(x)sin(y) ), but this is the angle I was given: ${-13\pi}/{12}$. How do I use a sum or difference formula to get the sin, cos, and tan of that?
  47. E

    Trigonometry: Analyzing and Graphing a Cosine Function

    Hey I need a second opinion to see if my formulas and calculations are correct. Also I need help with graphing this problem. My problem is to find amplitude, period, horizontal shift, vertical translation, step and then graph of: y= 2 - (1/3) cos ( πx + (3π/2) ) , -1/4 ≤ x ≤ 15/4 Using the...
  48. jpcyiu

    Is There a Trick to Remembering the Trigonometric Functions?

    hello everyone! I want to know how to verify cos sin tan I always feel confused when i am doing the physics exercises. are we always use cos when it is x-axis and use sin when it is y-axis?? I feel so confused.
  49. L

    Work & Energy: Forces with Angles

    Homework Statement A student could either push or pull, at an angle of 30 degrees from the horizontal, a 40kg crate, where the coefficient of kinetic friction is .21. The crate is moved 18m. Calculate the minimum work for pushing and pulling. Homework Equations W=F•(change in)X•cos(angle in...